The Archbishop made the announcement ten weeks ago as 84 Church of England bishops criticised David Cameron's government for ignoring their help to offer accommodation to around 50,000 refugees.
The Sunday Times has reported that officials at Lambeth Palace are so concerned about the delay that they came up with a back-up plan to invite Christian refugees from another diocese instead.
But they dropped this idea after worries were raised that it could single some families out and leave others behind.
Tim Finch, coordinator of the National Refugees Welcome Board said: "It's frustrating that voluntary offers to help house Syrians, like that made by the archbishop, aren't being taken up at the moment.
"Bureaucracy is getting in the way of generosity."
Alternative options to waiting for its local council to secure an allocation of refugees are now being explored.
Lambeth said: "We are currently working... with the Home Office in exploring our participation in the emerging community sponsorship programme.
"This will enable director community involvement in supporting Syrian refugees."
The Government has set a limit of taking in 20,000 Syrian refugees over five years.